Сандық өрнектерді тепе-тең түрлендіру (Рустюмова 1.1.1А (1-16))

Шешуі: $${1,133:1,1 = \dfrac{{1133}}{{1000}} \cdot \dfrac{{10}}{{11}} = \dfrac{{1100 + 33}}{{100 \cdot 11}} = \dfrac{{103}}{{100}} = 1,03}$$ $${1,03 - 1,2 = - 0,17}$$ $${ - 0,17:( - 0,02) \cdot 0,2 = \dfrac{{17}}{{100}} \cdot \dfrac{{100}}{2} \cdot \dfrac{2}{{10}} = 1,7}$$ $${3,7 - 1,7 = 2}$$

Шешуі: $$ = \dfrac{{(4,3 - 0,4) \cdot 0,25}}{{\dfrac{{25}}{{16}} \cdot \dfrac{2}{5} + \dfrac{3}{8} \cdot \dfrac{1}{3}}} = \dfrac{{3,9 \cdot 0,25}}{{\dfrac{5}{8} + \dfrac{1}{8}}} = \dfrac{{3,9 \cdot \dfrac{1}{4}}}{{\dfrac{6}{8}}} = \dfrac{{3,9 \cdot \dfrac{1}{4}}}{{\dfrac{3}{4}}} = 1,3$$

Шешуі: $${ = \dfrac{8}{3}:\dfrac{{16}}{9} + \dfrac{{55}}{{84}}:\left( {\dfrac{{43}}{{9 \cdot 7}} - \dfrac{{23}}{{9 \cdot 4}}} \right) = \dfrac{8}{3} \cdot \dfrac{9}{{16}} + \dfrac{{55}}{{84}}:\dfrac{{43 \cdot 4 - 23 \cdot 7}}{{9 \cdot 7 \cdot 4}} = }$$ $${ = \dfrac{3}{2} + \dfrac{{55}}{{84}}:\dfrac{{9 \cdot 7 \cdot 4}}{{172 - 161}} = \dfrac{3}{2} + \dfrac{{55}}{3} \cdot \dfrac{9}{{11}} = \dfrac{3}{2} + 15 = 16,5}$$

Шешуі: $${ = \dfrac{{40}}{7} \cdot \dfrac{{21}}{8} + \dfrac{{21}}{{13}} \cdot \left( {\dfrac{{43}}{{8 \cdot 7}} - \dfrac{{11}}{{8 \cdot 3}}} \right) = 15 + \dfrac{{21}}{{13}} \cdot \left( {\dfrac{{43 \cdot 3 - 7 \cdot 11}}{{8 \cdot 7 \cdot 3}}} \right) = }$$ $${ = 15 + \dfrac{{21}}{{13}} \cdot \dfrac{{52}}{{8 \cdot 21}} = 15 + \dfrac{4}{8} = 15,5}$$

Шешуі: $${ = \dfrac{{41 \cdot 2 - 17}}{{36}} \cdot \dfrac{{18}}{{65}} + \dfrac{{8 \cdot 7 - 23}}{{49}} \cdot \dfrac{{49}}{{99}} + \dfrac{7}{6} = \dfrac{{18}}{{36}} + \dfrac{{33}}{{99}} + \dfrac{7}{6} = }$$ $${ = \dfrac{1}{2} + \dfrac{1}{3} + \dfrac{7}{6} = \dfrac{{3 + 2 + 7}}{6} = \dfrac{{12}}{6} = 2}$$

Шешуі: $${ = \left( {\dfrac{1}{2} + \dfrac{1}{8} - \dfrac{1}{6}} \right) \cdot \left( {\dfrac{{32}}{5} \cdot \dfrac{3}{{80}}} \right) + \dfrac{1}{8} = }$$ $${ = \dfrac{{24 + 6 - 8}}{{48}} \cdot \dfrac{6}{{25}} + \dfrac{1}{8} = \dfrac{{22}}{{48}} \cdot \dfrac{6}{{25}} + \dfrac{1}{8} = \dfrac{{11}}{{4 \cdot 25}} + \dfrac{1}{8} = }$$ $${ = \dfrac{{110}}{{1000}} + \dfrac{{125}}{{1000}} = 0,235}$$

Шешуі: $${ = \left( {\dfrac{{20}}{3} + \dfrac{{34}}{{15}} + \dfrac{{11}}{2}} \right) \cdot 15 - 30 \cdot \dfrac{{28}}{5} = }$$ $${ = \dfrac{{20 \cdot 10 + 2 \cdot 34 + 15 \cdot 11}}{{30}} \cdot 15 - 6 \cdot 28 = }$$ $${\dfrac{{268 + 165}}{2} - 168 = 134 + \dfrac{{165}}{2} - 168 = 82\dfrac{1}{2} - 34 = 48\dfrac{1}{2}}$$

Шешуі: $${ = \left( {3\dfrac{{13}}{{15}} - 5\dfrac{4}{{45}} - \left( {12\dfrac{3}{{20}} + \dfrac{{85}}{{100}}} \right)} \right) \cdot 3 = \left( {3\dfrac{{39}}{{45}} - 4\dfrac{{49}}{{45}} - \left( {12\dfrac{3}{{20}} + \dfrac{{17}}{{20}}} \right)} \right) \cdot 3 = }$$ $${ = \left( { - 1\dfrac{{10}}{{45}} - 13} \right) \cdot 3 = - 14\dfrac{2}{9} \cdot 3 = - \dfrac{{126 + 2}}{9} \cdot 3 = - \dfrac{{128}}{3} = - 42\dfrac{2}{3}}$$

Шешуі: $${ = - 7,8 - 1,3 \cdot (14 - 20) = - 7,8 - 1,3 \cdot ( - 6) = }$$ $${ = - 7,8 + 7,8 = 0}$$

Шешуі: $${ = \left( {3,24 \cdot \dfrac{7}{9} - \dfrac{{16}}{5} \cdot \dfrac{3}{4}} \right) \cdot \dfrac{{10}}{9} = \left( {\dfrac{{324}}{{100}} \cdot \dfrac{7}{9} - \dfrac{{12}}{5}} \right) \cdot \dfrac{{10}}{9} = }$$ $${ = \left( {\dfrac{{81}}{{25}} \cdot \dfrac{7}{9} - \dfrac{{12}}{5}} \right) \cdot \dfrac{{10}}{9} = \left( {\dfrac{{63}}{{25}} - \dfrac{{12 \cdot 5}}{{25}}} \right) \cdot \dfrac{{10}}{9} = \dfrac{3}{{25}} \cdot \dfrac{{10}}{9} = \dfrac{2}{{15}}}$$

Шешуі: $$ = \dfrac{5}{{14}} \cdot \dfrac{{72}}{{25}} \cdot \dfrac{7}{{72}} \cdot \dfrac{{36}}{5} \cdot \dfrac{{25}}{{12}} = \dfrac{{18}}{2} = 9$$ Кері сан : $\dfrac{1}{9}$

Шешуі: $$\dfrac{{53}}{{22}} = 2,40909… = 2,4\left( {09} \right)$$

Шешуі:

Шешуі: $$2 \cdot 7 = 14$$

Шешуі: $$27 \cdot 2 \cdot 3 \cdot 5 \cdot 7 = 54 \cdot 105 = 5670$$

Шешуі: $$39 \cdot 2 \cdot 2 \cdot 5 \cdot 5 = 3900$$